We are faced with the paradoxical fact that education has become one of the chief obstacles to intelligence and freedom of thought.
Gradually, ... the aspect of science as knowledge is being thrust into the background by the aspect of science as the power of manipulating nature. It is because science gives us the power of manipulating nature that it has more social importance than art. Science as the pursuit of truth is the equal, but not the superior, of art. Science as a technique, though it may have little intrinsic value, has a practical importance to which art cannot aspire.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the georgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.
Mathematics is only the art of saying the same thing in different words.
It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty-a beauty cold and austere ... yet sublimely pure and capable of stern perfection such as only the greatest art can show.
Mankind is divided into two classes: those who, being artificial, praise nature, and those who, being natural, praise art.
There will still be things that machines cannot do. They will not produce great art or great literature or great philosophy; they will not be able to discover the secret springs of happiness in the human heart; they will know nothing of love and friendship.
The significance of a fact is relative to [the general body of scientific] knowledge. To say that a fact is significant in science, is to say that it helps to establish or refute some general law; for science, though it starts from observation of the particular, is not concerned essentially with the particular, but with the general. A fact, in science, is not a mere fact, but an instance. In this the scientist differs from the artist, who, if he deigns to notice facts at all, is likely to notice them in all their particularity.
The essence of education is that it is a change effected in the organism to satisfy the operator.
Ethics is in origin the art of recommending to others the sacrifices required for cooperation with oneself.
The main things which seem to me important on their own account, and not merely as means to other things, are knowledge, art, instinctive happiness, and relations of friendship or affection.
Philosophy, for Plato, is a kind of vision, the 'vision of truth'...Everyone who has done any kind of creative work has experienced, in a greater or less degree, the state of mind in which, after long labour, truth or beauty appears, or seems to appear, in a sudden glory - it may only be about some small matter, or it may be about the universe. I think that most of the best creative work, in art, in science, in literature, and in philosophy, has been a result of just such a moment.
In science the successors stand upon the shoulders of their predecessors; where one man of supreme genius has invented a method, a thousand lesser men can apply it. ... In art nothing worth doing can be done without genius; in science even a very moderate capacity can contribute to a supreme achievement.
[Freedom] is the greatest of political goods. I do not say freedom is the greatest of all goods: the best things come from within they are such things as creative art, and love, and thought. Such things can be helped or hindered by political conditions, but not actually produced by them; and freedom is, both in itself and in its relation to these other goods the best thing that political and economic conditions can secure.
You, your families, your friends and your countries are to be exterminated by the common decision of a few brutal but powerful men. To please these men, all the private affections, all the public hopes, all that has been achieved in art, and knowledge and thought and all that might be achieved hereafter is to be wiped out forever. Our ruined lifeless planet will continue for countless ages to circle aimlessly round the sun unredeemed by the joys and loves, the occasional wisdom and the power to create beauty which have given value to human life.
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